IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v25y2011i10p2543-2573.html
   My bibliography  Save this article

Water Resources Allocation Using Solution Concepts of Fuzzy Cooperative Games: Fuzzy Least Core and Fuzzy Weak Least Core

Author

Listed:
  • Mojtaba Sadegh
  • Reza Kerachian

Abstract

In this paper, two new solution concepts for fuzzy cooperative games, namely Fuzzy Least Core and Fuzzy Weak Least Core are developed. They aim for optimal allocation of available water resources and associated benefits to water users in a river basin. The results of these solution concepts are compared with the results of some traditional fuzzy and crisp games, namely Fuzzy Shapley Value, Crisp Shapley Value, Least Core, Weak Least Core and Normalized Nucleolus. It is shown that the proposed solution concepts are more efficient than the crisp games. Moreover, they do not have the limitation of Fuzzy Shapley Value in satisfying the group rationality criterion. This paper consists of two steps. In the first step, an optimization model is used for initial water allocation to stakeholders. In the second step, fuzzy coalitions are defined and participation rates of water users (players) in the fuzzy coalitions are optimized in order to reach a maximum net benefit. Then, the total net benefit is allocated to the players in a rational and equitable way using Fuzzy Least Core, Fuzzy Weak Least Core and some traditional fuzzy and crisp games. The effectiveness and applicability of the proposed methodology is examined using a numerical example and also applying it to the Karoon river basin in southern Iran. Copyright Springer Science+Business Media B.V. 2011

Suggested Citation

  • Mojtaba Sadegh & Reza Kerachian, 2011. "Water Resources Allocation Using Solution Concepts of Fuzzy Cooperative Games: Fuzzy Least Core and Fuzzy Weak Least Core," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(10), pages 2543-2573, August.
    • Handle: RePEc:spr:waterr:v:25:y:2011:i:10:p:2543-2573
    DOI: 10.1007/s11269-011-9826-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11269-011-9826-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11269-011-9826-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Shujin & Zhang, Qiang, 2009. "A simplified expression of the Shapley function for fuzzy game," European Journal of Operational Research, Elsevier, vol. 196(1), pages 234-245, July.
    2. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    3. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Tsurumi, Masayo & Tanino, Tetsuzo & Inuiguchi, Masahiro, 2001. "A Shapley function on a class of cooperative fuzzy games," European Journal of Operational Research, Elsevier, vol. 129(3), pages 596-618, March.
    5. Wang, Lizhong & Fang, Liping & Hipel, Keith W., 2008. "Basin-wide cooperative water resources allocation," European Journal of Operational Research, Elsevier, vol. 190(3), pages 798-817, November.
    6. Augusto Getirana & Valéria de Fátima Malta, 2010. "Investigating Strategies of an Irrigation Conflict," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(12), pages 2893-2916, September.
    7. Hanan Luss, 1999. "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach," Operations Research, INFORMS, vol. 47(3), pages 361-378, June.
    8. Raquel Salazar & Ferenc Szidarovszky & Abraham Rojano, 2010. "Water Distribution Scenarios in the Mexican Valley," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(12), pages 2959-2970, September.
    9. McKinney, D. C. & Cai, X. & Rosegrant, M. W. & Ringler, C. & Scott, C. A., 1999. "Modeling water resources management at the basin level: review and future directions," IWMI Books, Reports H024075, International Water Management Institute.
    10. Suman Sensarma & Norio Okada, 2010. "Redefining the Game in Local Water Management Conflict: A Case Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(15), pages 4307-4316, December.
    11. Mojtaba Sadegh & Najmeh Mahjouri & Reza Kerachian, 2010. "Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2291-2310, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Li Pan & Xudong Chen & Lu Zhao & Anran Xiao, 2019. "Does Information Asymmetry Impact Sub-Regions’ Cooperation of Regional Water Resource Allocation?," IJERPH, MDPI, vol. 16(21), pages 1-16, November.
    2. Narges Taravatrooy & Mohammad Reza Nikoo & Mojtaba Sadegh & Mohammad Parvinnia, 2018. "A hybrid clustering-fusion methodology for land subsidence estimation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(2), pages 905-926, November.
    3. Javier Alarcón & Alberto Garrido & Luis Juana, 2014. "Managing Irrigation Water Shortage: a Comparison Between Five Allocation Rules Based on Crop Benefit Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(8), pages 2315-2329, June.
    4. Mohammad Nikoo & Reza Kerachian & Akbar Karimi, 2012. "A Nonlinear Interval Model for Water and Waste Load Allocation in River Basins," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(10), pages 2911-2926, August.
    5. Mehrdad Ghorbani Mooselu & Mohammad Reza Nikoo & Nooshin Bakhtiari Rayani & Azizallah Izady, 2019. "Fuzzy Multi-Objective Simulation-Optimization of Stepped Spillways Considering Flood Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(7), pages 2261-2275, May.
    6. Hamidreza Manshadi & Mohammad Niksokhan & Mojtaba Ardestani, 2015. "A Quantity-Quality Model for Inter-basin Water Transfer System Using Game Theoretic and Virtual Water Approaches," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(13), pages 4573-4588, October.
    7. Mohammad Nikoo & Reza Kerachian & Hamed Poorsepahy-Samian, 2012. "An Interval Parameter Model for Cooperative Inter-Basin Water Resources Allocation Considering the Water Quality Issues," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(11), pages 3329-3343, September.
    8. Mehmet Kucukmehmetoglu & Abdurrahman Geymen, 2014. "Transboundary Water Resources Allocation under Various Parametric Conditions: The Case of the Euphrates & Tigris River Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3515-3538, September.
    9. Armaghan Abed-Elmdoust & Reza Kerachian, 2014. "Evaluating the Relative Power of Water Users in Inter-Basin Water Transfer Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(2), pages 495-509, January.
    10. Hamed Poorsepahy-Samian & Reza Kerachian & Mohammad Nikoo, 2012. "Water and Pollution Discharge Permit Allocation to Agricultural Zones: Application of Game Theory and Min-Max Regret Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 4241-4257, November.
    11. Keighobad Jafarzadegan & Armaghan Abed-Elmdoust & Reza Kerachian, 2013. "A Fuzzy Variable Least Core Game for Inter-basin Water Resources Allocation Under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(9), pages 3247-3260, July.
    12. Armaghan Abed-Elmdoust & Reza Kerachian, 2013. "Incorporating Economic and Political Considerations in Inter-Basin Water Allocations: A Case Study," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(3), pages 859-870, February.
    13. J. Alarcón & L. Juana, 2016. "The Water Markets as Effective Tools of Managing Water Shortages in an Irrigation District," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(8), pages 2611-2625, June.
    14. Mohammad S. Khorshidi & Mohammad Reza Nikoo & Mojtaba Sadegh & Banafsheh Nematollahi, 2019. "A Multi-Objective Risk-Based Game Theoretic Approach to Reservoir Operation Policy in Potential Future Drought Condition," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(6), pages 1999-2014, April.
    15. Armaghan Abed-Elmdoust & Reza Kerachian, 2012. "Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(13), pages 3961-3976, October.
    16. Ben Li & Guangming Tan & Gang Chen, 2016. "Generalized Uncooperative Planar Game Theory Model for Water Distribution in Transboundary Rivers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 225-241, January.
    17. Yizhong Chen & Li He & Hongwei Lu & Jing Li & Lixia Ren, 2018. "Planning for Regional Water System Sustainability Through Water Resources Security Assessment Under Uncertainties," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(9), pages 3135-3153, July.
    18. Najmeh Mahjouri & Mohammad Bizhani-Manzar, 2013. "Waste Load Allocation in Rivers using Fallback Bargaining," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2125-2136, May.
    19. Mohammad Reza Nikoo & Pouyan Hatami Bahman Beiglou & Najmeh Mahjouri, 2016. "Optimizing Multiple-Pollutant Waste Load Allocation in Rivers: An Interval Parameter Game Theoretic Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4201-4220, September.
    20. Zhenliang Liao & Phillip Hannam, 2013. "The Mekong Game: Achieving an All-win Situation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2611-2622, May.
    21. Shahin Zandmoghaddam & Ali Nazemi & Elmira Hassanzadeh & Shadi Hatami, 2019. "Representing Local Dynamics of Water Resource Systems through a Data-Driven Emulation Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3579-3594, August.
    22. Alireza Mojarabi-Kermani & Ehsan Shirangi & Amin Bordbar & Amir Abbas Kaman Bedast & Alireza Masjedi, 2019. "Stochastic Optimal Reservoir Operation Management, Applying Group Conflict Resolution Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(8), pages 2847-2865, June.
    23. Chunlong Li & Jianzhong Zhou & Shuo Ouyang & Chao Wang & Yi Liu, 2015. "Water Resources Optimal Allocation Based on Large-scale Reservoirs in the Upper Reaches of Yangtze River," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(7), pages 2171-2187, May.
    24. Ben Li & Guangming Tan & Gang Chen, 2016. "Generalized Uncooperative Planar Game Theory Model for Water Distribution in Transboundary Rivers," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 225-241, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mojtaba Sadegh & Najmeh Mahjouri & Reza Kerachian, 2010. "Optimal Inter-Basin Water Allocation Using Crisp and Fuzzy Shapley Games," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(10), pages 2291-2310, August.
    2. Liu, Dehai & Ji, Xiaoxian & Tang, Jiafu & Li, Hongyi, 2020. "A fuzzy cooperative game theoretic approach for multinational water resource spatiotemporal allocation," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1025-1037.
    3. Elahe Fallah-Mehdipour & Omid Bozorg Haddad & Soheila Beygi & Miguel Mariño, 2011. "Effect of Utility Function Curvature of Young’s Bargaining Method on the Design of WDNs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(9), pages 2197-2218, July.
    4. Armaghan Abed-Elmdoust & Reza Kerachian, 2012. "Water Resources Allocation Using a Cooperative Game with Fuzzy Payoffs and Fuzzy Coalitions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(13), pages 3961-3976, October.
    5. Ciftci, B.B., 2009. "A cooperative approach to sequencing and connection problems," Other publications TiSEM b0f08a17-4734-4d57-ad66-f, Tilburg University, School of Economics and Management.
    6. Harald Wiese, 2012. "Values with exogenous payments," Theory and Decision, Springer, vol. 72(4), pages 485-508, April.
    7. Yu-Hsien Liao, 2017. "Fuzzy games: a complement-consistent solution, axiomatizations and dynamic approaches," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 257-268, September.
    8. Nils Roehl, 2013. "Two-Stage Allocation Rules," Working Papers Dissertations 01, Paderborn University, Faculty of Business Administration and Economics.
    9. Reiner Wolff, 2007. "Eine spieltheoretische Analyse des Länderfinanzausgleichs in der Bundesrepublik Deutschland," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 27(1), pages 89-101, February.
    10. Kaveh Madani & Keith Hipel, 2011. "Non-Cooperative Stability Definitions for Strategic Analysis of Generic Water Resources Conflicts," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(8), pages 1949-1977, June.
    11. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    12. Barış Çiftçi & Peter Borm & Herbert Hamers, 2010. "Population monotonic path schemes for simple games," Theory and Decision, Springer, vol. 69(2), pages 205-218, August.
    13. Zhuowei Shen & Pan Liu & Bo Ming & Maoyuan Feng & Xiaoqi Zhang & He Li & Aili Xie, 2018. "Deriving Optimal Operating Rules of a Multi-Reservoir System Considering Incremental Multi-Agent Benefit Allocation," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(11), pages 3629-3645, September.
    14. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 2017. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 26(3), pages 565-595, May.
    15. Sapi, Geza, 2012. "Bargaining, vertical mergers and entry," DICE Discussion Papers 61, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    16. Gustavo Bergantiños & Juan Vidal-Puga, 2005. "The Consistent Coalitional Value," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 832-851, November.
    17. van den Brink, René & González-Arangüena, Enrique & Manuel, Conrado & del Pozo, Mónica, 2014. "Order monotonic solutions for generalized characteristic functions," European Journal of Operational Research, Elsevier, vol. 238(3), pages 786-796.
    18. Ciftci, B.B. & Dimitrov, D.A., 2006. "Stable Coalition Structures in Simple Games with Veto Control," Other publications TiSEM fd2410e3-8e9d-4319-86fb-b, Tilburg University, School of Economics and Management.
    19. Jacob North Clark & Stephen Montgomery-Smith, 2018. "Shapley-like values without symmetry," Papers 1809.07747, arXiv.org, revised May 2019.
    20. Tido Takeng, Rodrigue, 2022. "Uncertain production environment and communication structure," Journal of Mathematical Economics, Elsevier, vol. 102(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:waterr:v:25:y:2011:i:10:p:2543-2573. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.